Monday, June 19, 2006

Holistic Rationality

I'm currently working an essay exploring my (perhaps slightly wacky) distinction between the 'local' (atomistic) and 'global' (holistic) levels of rationality. Here's the core idea:

Global optimality may sometimes require us to do other than what seems optimific within the confines of a moment. Holistic rationality, as I envisage it, tells us to adopt a broader view, transcending the boundaries of the present and identifying with a timeless perspective instead. It further requires that we be willing to treat the dictates of this broader perspective as rationally authoritative, no matter how disadvantageous this may seem from the particular perspective of the present moment. This amounts to an intrapersonal analogue of the ‘social contract’: each of our momentary stages abdicates some degree of rational autonomy, in order to enhance the rationality and autonomy of our person as a whole.

I initially thought this mapped onto the distinction between 'direct' and 'indirect' rationality, where the former perspective is effectively limited to considering only immediate evidence and first-order judgments. But that's not quite right. The local perspective of a momentary person-stage can (and should) let higher-order judgments of reliability influence their present expected utility judgments, and thus metacoherence should lead them to embrace an "all things considered" indirect strategy even within the confines of the moment.

The local/global distinction is better illustrated by the sorts of rational "paradoxes" which suggest trouble for the former perspective:

Pollock’s Ever Better Wine improves with age, without limit. Suppose you possess a bottle, and are also immortal. When should you drink the wine? Local rationality implies that you should never drink it, for at any given time you would do better to postpone it another day. But to never drink it at all is the worst possible result! Or consider Quinn’s Self-Torturer, who receives $10,000 each time he increases his pain level by an indiscernible increment. It sounds like a deal worth taking. But suppose that the combined effect of a thousand increments would leave him in such agony that no amount of money could compensate. Because each individual increment is - from the local perspective of the moment - worth taking, local rationality will again lead one to the worst possible result.

A good result is only possible for agents who are willing to let their global perspective override local calculations. The agent must make in advance a rational resolution to stop at some stage n, even though from the local perspective of stage n he would do better to continue on to stage n+1. It seems clear that the global perspective is rationally preferable. The agent can foresee the outcomes of his possible choices. If he endorses the local mode of reasoning then he will never stop, and so will end up with the worst possible outcome. It cannot be rational to accept this when other options are open to him. If he is instead resolute and holds firm to the choice - made from a global or timeless perspective - to stop at stage n, then he will do much better.

Convinced?

I find something intuitively appealing about the idea that persons can abstract away from their particular momentary stage, and make decisions from a 'timeless' perspective instead. This holistic approach seems to ascribe a greater unity to persons than one finds in the standard atomistic view which pits our past and future stages against each other, as if they were wholly distinct and independent agents. Better to identify the agent as the whole, temporally extended person, and have each of our momentary selves conceive of themselves as mere parts of the whole, contributing to this "higher cause" without the presumption of total momentary autonomy -- we should have greater respect for our past reasons than that. In turn, it enables a stronger trust in one's future stages.

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15 comments:

1) I don’t know why you want (as opposed to it just being the case) to ascribe the greater unity of person as opposed to any other sort. That seems to have a hint of "un-utilitarianism" to me.

2) I’m not sure why the present me and the future me would be "pitted" against each other. I am pretty fond of the future me - he's a great guy (or I’d try to change). I care about his welfare equally to my own (maybe even more!) – even if he is just a copy of me... how utilitarian of me!

3) Should I seek perspectives that make me have more confidence in my own views despite not changing any of the facts? Should I want to see myself as right (even if that has no effect on the truth?) Hmmm.... I don’t know.

Also just to see what I can do with the examples..Does Pollock’s Ever Better Wine rely upon the infinity issue (ie you can propose a hypothetical that places the thing you want to "factor out" at infinity and you can come to the opposite conclusion – should work on anything) and Quinn’s Self-Torturer rely upon the irrationality of preference (i.e. that normal mathmatical operations don't always hold - or that you could propose a hypothetical where they don't)i.e. 100*10,000 <100*(-poison) but 10,000>(-poison). Rather like how I could theoretically like apples more than oranges and oranges more than pears and pears more than apples. Choosing a appropriate hypothetical person you should be able to apply this to anything also.

Re: #2, it's not your interests, but your decisions (or rational autonomy) which are in conflict. That is, you current self decides just to go so far as n but then stop, whereas your future self decides that each n+1 is better than the n you're at, and so overrides your earlier resolution.

I'm not sure where your #3 came from or how it's relevant.

Regarding the examples, I agree that EBW depends on "the infinity issue", and we could easily come up with other cases which follow the same general template. But again, I'm not clear on the relevance (unless you think examples involving the infinite are necessarily illegitimate?), since it seems like a genuinely possible scenario which decision theory should be able to make sense of. So I think it makes a pretty strong case in favour of the global perspective, or the need for binding "rational resolutions".

The self-torturer case involve intransitive preferences, it's true, but there doesn't seem to be anything irrational about it (unlike your fruit case). Rather, intransitive preferences seem the appropriate response to the facts of the case, since we're told that individual increments are indiscernible but collectives of them are not. Again, this seems like a possible scenario, and our theories ought to apply sensibly to it. The fact that they don't (e.g. your maths equation) show that there's something wrong with our present theories, not that there's anything wrong with the scenarios. (They're more like the raw data that any adequate theory has to explain.)

> Whereas your future self decides that each n+1 is better than the n you're at, and so override your earlier resolution.

I still don’t see that as pitting anything against anything else. I guess I have a considerable amount of trust in the future me.

>I'm not sure where you’re #3 came from or how it's relevant.

Oh you just said in your last sentence "In turn, it enables a stronger trust in one's future stages."

> But again, I'm not clear on the relevance

It permits reducto ad absurdum.

Let’s say you have an example where the benefits of global reasoning are experienced at infinity and the benefits of local thinking are experienced now. I’ll try to do an example when I have more time.

> But there doesn't seem to be anything irrational about it (unlike your fruit case).

Defining the increments to be the same as 0 is not separate from the rationality of preferences question - it is part of it. It is the sort of reasoning that lies behind any irrational preference. What you have done is separated out the “irrationality” – but still left it in the hypothetical (which changes nothing).

One interesting hypothetical is if you believe in the Plutonium Rule as per your religion and there are an infinite number of people (or a pause that could in any sense be considered infinite, which surely it could be) and god's experience of lives was random (not required but makes it clearer) then your religion would fail to have any substantive conclusion (because every other life is infinitely in your "future" or "past").

Philosophical arguments using infinity are notoriously imprecise. This is not to say that all statements about infinity are imprecise, just that it's a very difficult subject that took until the late 19th century to be properly understood, and the 20th century for most of the ancient dilemmas to be resolved. In most cases the resolution flows quite naturally for greater precision in the use of language. So be very careful presenting these kinds of arguments to philosophers who have mathematical training, or you'll get into a shitfight that it will take you weeks to understand even how you lost.

I don't know if you have that training already. I only make the comment because so few philosophers have bothered with the mathematics of the infinite. And those that have are not usually the top scholars in the field!

Genius, sorry to say it, but I thought you were totally guilty of what I was saying.

Why? Because you seem to be saying that God could not visit an infinite number of people, or even an appreciable fraction thereof, by your selection process. You seem to imply this is true for every selection process, including sequential methods.

But if God has infinite time to work in, he not only could, he certainly will visit everyone, even if the number of people is infinite. Furthermore, since God is standing outside of time, he already has. That is how I read 'Richard's Religion'.

And the one objection I have to that religion is to note the incredible ungodliness of just about everyone! I could be misunderstanding it, but it would seem to me that if God's already in all of us, he's got a lot to learn himself.

But it's a 'normative' religion, surely? Meaning it's not meant to be argued for as actually true, but treated as though it was true, for the effect that creates? Which would be everyone would try to act like Jesus? Apart from miracles, that does seem to be the teaching of more orthodox christianity!

"It was a reducto ad absurdium!I want him to either reject his usage of infinity or reject a deeply held belief - the idea being the former will be the one to loose."

I don't follow it, though. The use of infinity seems ok to me. Except in so far as being totally contradicted by observation, since most people are not a bit godly, and god would have visited all of them an infinite number of times if he was doing it randomly for infinite time.

Or are you trying to say the very fact the world is not up to deity standards is proof that if a god is playing this game then he can't have been doing it for infinite time?

My solution to the infinity issue is 1) Rather like, I guess, your position - you can (sometimes) engage in infinity maths i.e. canceling infinities and declaring one to be bigger than another or equal to another. and thus you do have to take into account events at infinity.

2) Infinities are best thought of as limits or with the usual sorts of "greater infinity" "lesser infinity" sort of approaches (the usual sort of tools) and in this way we can manipulate them. Richard seems to generally reject this and define the solution to any such problem as undefined.

3) Not so relevant to this debate and most controversially - I think that the universe can handle contradictions involving scenarios that cant exist (for example there could be a law saying the world will turn into a cream doughnut if up becomes down, or after a period somewhat longer than the life of the universe, and that wouldn't cause any problems at all).

EitherA) The error that creates the infinity in the hypothetical also has the potential to destroy the solutionorB) Many infinity examples use sorts of infinity that cannot exist and thus asking a question about what happens in that case is not something the universe has to resolve, the “quantum waves” don’t have to converge, if you like.

Like I said, I don't quite get what you say is contradictory. Using infinities in arguments is perfectly OK, even if it's usually done in a hamfisted way that just shows imprecision in language use, and unawareness of the high level of development the field has actually gone through in the last 150 years. But a hamfisted general application doesn't mean a perfectly valid specific application is impossible.

With respect to contradictions, saying the universe can handle them is another imprecision in the use of language. Contradicion is a feature of logical systems. Usually a bad feature that we seek to remove, since in any system with contradictions "anything goes". That is why the most usual conclusion from finding a contradiction in a system S is to conclude ~S.

The universe can't be 'contradictory'. The word just doesn't apply. Our theories about the universe can be, but that is hardly the universe's fault. We make a gross assumption that the universe is 'ordered' and follows laws. Perhaps it isn't and doesn't. That doesn't make it contradictory, just unpredictable. And any arguments using infinity as thought experiments about the actual universe run the same gauntlet of assuming an infinity that may not exist. Perhaps the universe is not infinite in either space or time. Infinity arguments can only be guaranteed to apply to logical systems, and there they apply perfectly well.

So, sorry to be a pedant, but this does interest me. Perhaps you're a step ahead. Why do you think there is "error that creates the infinity in the hypothetical"?

I seem to be saying the same as you most of the time (but possibly not very clearly!).

> That is why the most usual conclusion from finding a contradiction in a system S is to conclude ~S.

I agree yes that a contradiction (in a hypothetical of course since it wouldn’t exist in reality) implies there is something wrong. And as you seem to agree it may mean that X (some other random thing in the system) is impossible. When you put infinity into an equation when you know full well that that infinity is likely to be impossible (e.g. a man who lives forever) you already have a potential candidate.

> Why do you think there is "error that creates the infinity in the hypothetical"?

The error might be "that a man can live forever" - based on ignoring things like entropy or any other laws that would control the system.

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